Methods2026 NHT Exam 2 Section A · Q19CAS active1 mark

Conditional probability of winning a free throw game

A basketball player has three attempts to score from the free throw line. If the player scores at least twice, they win the game.

Assume that for each attempt, the probability that the player will score is $p$ , where $0 < p < 1$ . The outcome of each attempt is independent of all others.

Given that the player wins the game, the probability that exactly one of the first two attempts was missed is given by

1 mark

\dfrac{1-p}{3-2p}

\dfrac{1-p}{p(3-2p)}

\dfrac{2(1-p)}{3-2p}

\dfrac{2(1-p)}{p(3-2p)}

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